Search results for "Eulerian path"
showing 10 items of 25 documents
The impacts of the ALE and hydrostatic-pressure approaches on the energy budget of unsteady free-surface flows
2008
Abstract This paper focuses on the energy budget in the calculation of unsteady free-surface flows on moving grids with and without using the ‘arbitrary Lagrangian–Eulerian’ (ALE) formulation or hydrostatic-pressure assumption. The numerical tool is an in-house general-purpose solver for the unsteady, incompressible and homogeneous Navier–Stokes equations in a Cartesian domain. An explicit fractional-step method and co-located finite-volume method are used for the second-order accurate integrations in time and space. The test cases are nonlinear and linear irrotational standing waves, which allow to characterise the impacts of an ALE or Eulerian formulation with moving grids by comparison w…
The pruning-grafting lattice of binary trees
2008
AbstractWe introduce a new lattice structure Bn on binary trees of size n. We exhibit efficient algorithms for computing meet and join of two binary trees and give several properties of this lattice. More precisely, we prove that the length of a longest (resp. shortest) path between 0 and 1 in Bn equals to the Eulerian numbers 2n−(n+1) (resp. (n−1)2) and that the number of coverings is (2nn−1). Finally, we exhibit a matching in a constructive way. Then we propose some open problems about this new structure.
A comparison of numerical surface topography calculations in geodynamic modelling: an evaluation of the ‘sticky air’ method
2012
SUMMARY Calculating surface topography in geodynamic models is a common numerical problem. Besides other approaches, the so-called ‘sticky air’ approach has gained interest as a free-surface proxy at the top boundary. The often used free slip condition is thereby vertically extended by introducing a low density, low viscosityfluid layer. This allows the air/crust interface to behave in a similar manner to a true free surface. We present here a theoretical analysis that provides the physical conditions under which the sticky air approach is a valid approximation of a true free surface. Two cases are evaluated that characterize the evolution of topography on different timescales: (1) isostati…
Prediction of flow patterns during silo discharges using a finite element approach and its preliminary experimental verification
2015
Abstract Obtaining a reliable discharge of particulate solids from a storage silo is a prerequisite to securing operational adequacy in solids handling processes. If a silo is poorly designed, an unreliable interrupted discharge often occurs. In this study, an in-house finite element (FE) program was modified to predict the particulate solids flow patterns during discharges from silos, and the effect of a double-cone insert on such flow patterns. In FE modeling, a Eulerian approach was adopted with an assumption of steady-state flow—a state that greatly facilitated investigations on the effects of double-cone inserts on the flow of particulate solids. Predictions were carried out on whether…
Eulerian models of the rotating flexible wheelset for high frequency railway dynamics
2019
Abstract In this paper three formulations based on an Eulerian approach are presented to obtain the dynamic response of an elastic solid of revolution, which rotates around its main axis at constant angular velocity. The formulations are especially suitable for the study of the interaction of a solid with a non-rotating structure, such as occurs in the coupled dynamics of a railway wheelset with the track. With respect to previous publications that may adopt similar hypotheses, this paper proposes more compact formulations and eliminates certain numerical problems associated with the presence of second-order derivatives with respect to the spatial coordinates. Three different models are dev…
Galaxy cluster mergers
2009
We present the results of an Eulerian adaptive mesh refinement (AMR) hydrodynamical and N-body simulation in a $\Lambda$CDM cosmology. The simulation incorporates common cooling and heating processes for primordial gas. A specific halo finder has been designed and applied in order to extract a sample of galaxy clusters directly obtained from the simulation without considering any resimulating scheme. We have studied the evolutionary history of the cluster halos, and classified them into three categories depending on the merger events they have undergone: major mergers, minor mergers, and relaxed clusters. The main properties of each one of these classes and the differences among them are di…
On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes
2016
We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfven waves, and the tearing mode instability using the MHD code Aenus. By comparing the simu- lation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of tearing modes we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast-magnetosonic speed and wavelength are the characteristic velocity and length, respectively, of the aforementioned (relatively simple) syst…
An introduction to relativistic hydrodynamics
2007
We review formulations of the equations of (inviscid) general relativistic hydrodynamics and (ideal) magnetohydrodynamics, along with methods for their numerical solution. Both systems can be cast as first-order, hyperbolic systems of conservation laws, following the explicit choice of an Eulerian observer and suitable fluid and magnetic field variables. During the last fifteen years, the so-called (upwind) high-resolution shock-capturing schemes based on Riemann solvers have been successfully extended from classical to relativistic fluid dynamics, both special and general. Nowadays, general relativistic hydrodynamical simulations in relativistic astrophysics are routinely performed, partic…
The structure of cosmic voids in a LCDM Universe
2013
Eulerian cosmological codes are especially suited to properly describe the low density regions. This property makes this class of codes excellent tools to study the formation and evolution of cosmic voids. Following such ideas, we present the results of an Eulerian adaptive mesh refinement (AMR) hydrodynamical and N-body simulation, that contrary to the common practice, has been designed to refine the computational grid in the underdense regions of the simulated volume. Thus, the void regions are better described due to the combined effect of the Eulerian character of the numerical technique and the use of high numerical resolution from the AMR approach. To analyse the outcome of this simul…
Influence of the porosity profile and sets of Ergun constants on the main hydrodynamic parameters in the trickle-bed reactors
2014
Abstract The Eulerian multiphase code has been applied for the comparative simulation of the experimental results obtained for varying flow rates of both fluid phases and for systems of various physicochemical properties used in the laboratory trickle-bed reactor (TBR). Therefore six different radial porosity profiles and three sets of the Ergun constants used in the relations defining the interphase momentum exchange have been implemented into the CFD code. The mean relative error of the pressure drop and of the averaged holdup as well as the standard deviation determined with respect to the experiments have been used as the criterion for the validation of the theoretical model. These valu…